Waring-Goldbach problems for unlike powers with almost equal variables

doi:10.1007/s11464-016-0512-4

Front. Math. China

2016, Vol. 11

Issue (2) : 449-460 https://doi.org/10.1007/s11464-016-0512-4

RESEARCH ARTICLE

Waring-Goldbach problems for unlike powers with almost equal variables

Meng ZHANG(

)

School of Mathematics, Shandong University, Jinan 250100, China

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Abstract

We prove that almost all positive even integers n can be written as n=p22+p33+p44+p55 with |pkk-N4|≤N321325+? for 2≤k≤5. Moreover, it is proved that each sufficiently large odd integer N can be represented as N=p1+p22+p33+p44+p55 with |pkk-N5|≤N321325+?for 1≤k≤5.

Keywords Exceptional set ofWaring-Goldbach problem exponential sum over primes in short intervals circle method

Corresponding Author(s): Meng ZHANG

Issue Date: 18 April 2016

Cite this article:

Meng ZHANG. Waring-Goldbach problems for unlike powers with almost equal variables[J]. Front. Math. China, 2016, 11(2): 449-460.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-016-0512-4
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I2/449

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